Department of Energy in 1982; that version is now known as DOE Macsyma. A copy of DOE Macsyma was maintained by Professor William F. Schelter of the University of Texas from 1982 until his death in 2001. In 1998, Schelter obtained permission from the Department of Energy to release the DOE Macsyma source code under the GNU Public License, and in 2000 he initiated the Maxima project at SourceForge to maintain and develop DOE Macsyma, now called Maxima.
Short Contents
1 Introduction to Maxima
. . . .
12 Bug Detection and Reporting
. . . .
73 Help
. . . .
114 Command Line
. . . .
155 Data Types and Structures
. . . .
416 Expressions
. . . .
857 Operators
. . . .
1118 Evaluation
. . . .
1319 Simplification
. . . .
14310 Mathematical Functions
. . . .
16111 Maxima’s Database
. . . .
18912 Plotting
. . . .
20913 File Input and Output
. . . .
24114 Polynomials
. . . .
25715 Special Functions
. . . .
28716 Elliptic Functions
. . . .
31317 Limits
. . . .
31918 Differentiation
. . . .
32119 Integration
. . . .
33520 Equations
. . . .
35721 Differential Equations
. . . .
37722 Numerical
. . . .
38123 Matrices and Linear Algebra
. . . .
39924 Affine
. . . .
42525 itensor
. . . .
42926 ctensor
. . . .
46327 atensor
. . . .
49128 Sums, Products, and Series
. . . .
49529 Number Theory
. . . .
51530 Symmetries
. . . .
53731 Groups
. . . .
55532 Runtime Environment
. . . .
55733 Miscellaneous Options
. . . .
56535 Sets
. . . .
58536 Function Definition
. . . .
60937 Program Flow
. . . .
64138 Debugging
. . . .
65739 alt-display
. . . .
66540 asympa
. . . .
67141 augmented lagrangian
. . . .
67342 Bernstein
. . . .
67543 bitwise
. . . .
67744 bode
. . . .
68145 celine
. . . .
68546 clebsch gordan
. . . .
68747 cobyla
. . . .
68948 combinatorics
. . . .
69349 contrib ode
. . . .
69950 descriptive
. . . .
70551 diag
. . . .
73952 distrib
. . . .
74553 draw
. . . .
77954 drawdf
. . . .
89755 dynamics
. . . .
90156 engineering-format
. . . .
91557 ezunits
. . . .
91758 f90
. . . .
93559 finance
. . . .
93760 fractals
. . . .
94361 ggf
. . . .
94762 graphs
. . . .
94963 grobner
. . . .
97964 hompack
. . . .
98765 impdiff
. . . .
99166 interpol
. . . .
99367 lapack
. . . .
100168 lbfgs
. . . .
100969 lindstedt
. . . .
101571 lsquares
. . . .
103172 minpack
. . . .
104173 makeOrders
. . . .
104374 mnewton
. . . .
104575 numericalio
. . . .
104776 odepack
. . . .
105377 operatingsystem
. . . .
105778 opsubst
. . . .
105979 orthopoly
. . . .
106180 pytranslate
. . . .
107381 ratpow
. . . .
107982 romberg
. . . .
108183 simplex
. . . .
108584 simplification
. . . .
108985 solve rec
. . . .
109986 stats
. . . .
110587 stirling
. . . .
112388 stringproc
. . . .
112589 to poly solve
. . . .
114990 unit
. . . .
116991 wrstcse
. . . .
117992 zeilberger
. . . .
118393 Error and warning messages
. . . .
118794 Command-line options
. . . .
1191A Function and Variable Index
. . . .
1193Table of Contents
1 Introduction to Maxima . . . . 1
2 Bug Detection and Reporting . . . . 7
2.1 Functions and Variables for Bug Detection and Reporting. . . 7
3 Help . . . . 11
3.1 Documentation. . . 11
3.2 Functions and Variables for Help. . . .11
4 Command Line . . . . 15
4.1 Introduction to Command Line. . . 15
4.2 Functions and Variables for Command Line. . . .15
4.3 Functions and Variables for Display. . . .25
5 Data Types and Structures . . . . 41
5.1 Numbers. . . 41
5.1.1 Introduction to Numbers. . . 41
5.1.2 Functions and Variables for Numbers. . . 41
5.2 Strings. . . 47
5.2.1 Introduction to Strings. . . 47
5.2.2 Functions and Variables for Strings. . . 47
5.3 Constants. . . 50
5.3.1 Functions and Variables for Constants. . . 50
5.4 Lists. . . 53
5.4.1 Introduction to Lists. . . .53
5.4.2 Functions and Variables for Lists. . . .53
5.4.3 Performance considerations for Lists. . . 70
5.5 Arrays. . . 72
5.5.1 Functions and Variables for Arrays. . . .72
5.6 Structures. . . .82
5.6.1 Introduction to Structures. . . 82
5.6.2 Functions and Variables for Structures. . . 82
6 Expressions . . . . 85
6.1 Introduction to Expressions. . . .85
6.2 Nouns and Verbs. . . 85
6.3 Identifiers. . . 86
6.4 Inequality. . . 87
6.5 Functions and Variables for Expressions. . . .87
7.1 Introduction to operators. . . .111
7.2 Arithmetic operators. . . 113
7.3 Relational operators. . . .117
7.4 Logical operators. . . .118
7.5 Operators for Equations. . . .119
7.6 Assignment operators. . . 121
7.7 User defined operators. . . .126
8 Evaluation . . . . 131
8.1 Functions and Variables for Evaluation. . . 131
9 Simplification . . . . 143
9.1 Introduction to Simplification. . . .143
9.2 Functions and Variables for Simplification. . . 145
10 Mathematical Functions . . . . 161
10.1 Functions for Numbers. . . .161
10.2 Functions for Complex Numbers. . . .166
10.3 Combinatorial Functions. . . 170
10.4 Root, Exponential and Logarithmic Functions. . . 173
10.5 Trigonometric Functions. . . .180
10.5.1 Introduction to Trigonometric. . . 180
10.5.2 Functions and Variables for Trigonometric. . . 180
10.6 Random Numbers. . . .187
11 Maxima’s Database . . . . 189
11.1 Introduction to Maxima’s Database. . . .189
11.2 Functions and Variables for Properties. . . .189
11.3 Functions and Variables for Facts. . . .198
11.4 Functions and Variables for Predicates. . . .205
12 Plotting . . . . 209
12.1 Introduction to Plotting. . . .209
12.2 Plotting Formats. . . .209
12.3 Functions and Variables for Plotting. . . .210
12.4 Plotting Options. . . 227
12.5 Gnuplot Options. . . 236
12.6 Gnuplot pipes Format Functions. . . 239
13 File Input and Output . . . . 241
13.1 Comments. . . 241
13.2 Files. . . .241
13.3 Functions and Variables for File Input and Output. . . .242
13.4 Functions and Variables for TeX Output. . . .249
13.5 Functions and Variables for Fortran Output. . . 254
14.1 Introduction to Polynomials. . . .257
14.2 Functions and Variables for Polynomials. . . .257
15 Special Functions . . . . 287
15.1 Introduction to Special Functions. . . .287
15.2 Bessel Functions. . . 287
15.3 Airy Functions. . . .290
15.4 Gamma and factorial Functions. . . 291
15.5 Exponential Integrals. . . .303
15.6 Error Function. . . .305
15.7 Struve Functions. . . 306
15.8 Hypergeometric Functions. . . .306
15.9 Parabolic Cylinder Functions. . . .307
15.10 Functions and Variables for Special Functions. . . 307
16 Elliptic Functions . . . . 313
16.1 Introduction to Elliptic Functions and Integrals. . . .313
16.2 Functions and Variables for Elliptic Functions. . . 314
16.3 Functions and Variables for Elliptic Integrals. . . 316
17 Limits . . . . 319
17.1 Functions and Variables for Limits. . . .319
18 Differentiation . . . . 321
18.1 Functions and Variables for Differentiation. . . .321
19 Integration . . . . 335
19.1 Introduction to Integration. . . .335
19.2 Functions and Variables for Integration. . . .335
19.3 Introduction to QUADPACK. . . .345
19.3.1 Overview. . . .346
19.4 Functions and Variables for QUADPACK. . . .347
20 Equations . . . . 357
20.1 Functions and Variables for Equations. . . .357
21 Differential Equations . . . . 377
21.1 Introduction to Differential Equations. . . 377
21.2 Functions and Variables for Differential Equations. . . 377
22.1 Introduction to fast Fourier transform. . . .381
22.2 Functions and Variables for fft. . . .381
22.3 Functions and Variables for FFTPACK5. . . .385
22.4 Functions for numerical solution of equations. . . 387
22.5 Introduction to numerical solution of differential equations. . .389
22.6 Functions for numerical solution of differential equations. . . . .390
23 Matrices and Linear Algebra . . . . 399
23.1 Introduction to Matrices and Linear Algebra. . . .399
23.1.1 Dot. . . 399
23.1.2 Matrices. . . 399
23.1.3 Vectors. . . .400
23.1.4 eigen. . . .400
23.2 Functions and Variables for Matrices and Linear Algebra. . . . .400
24 Affine . . . . 425
24.1 Introduction to Affine. . . .425
24.2 Functions and Variables for Affine. . . .425
25 itensor . . . . 429
25.1 Introduction to itensor. . . 429
25.1.1 New tensor notation. . . .430
25.1.2 Indicial tensor manipulation. . . .430
25.2 Functions and Variables for itensor. . . 433
25.2.1 Managing indexed objects. . . 433
25.2.2 Tensor symmetries. . . 442
25.2.3 Indicial tensor calculus. . . 444
25.2.4 Tensors in curved spaces. . . .448
25.2.5 Moving frames. . . 451
25.2.6 Torsion and nonmetricity. . . .454
25.2.7 Exterior algebra. . . .457
25.2.8 Exporting TeX expressions. . . 460
25.2.9 Interfacing with ctensor. . . 461
25.2.10 Reserved words. . . 462
26 ctensor . . . . 463
26.1 Introduction to ctensor. . . .463
26.2 Functions and Variables for ctensor. . . .465
26.2.1 Initialization and setup. . . .465
26.2.2 The tensors of curved space. . . .468
26.2.3 Taylor series expansion. . . 470
26.2.4 Frame fields. . . .473
26.2.5 Algebraic classification. . . 473
26.2.6 Torsion and nonmetricity. . . .476
26.2.7 Miscellaneous features. . . .477
26.2.9 Variables used byctensor. . . .485
26.2.10 Reserved names. . . .488
26.2.11 Changes. . . 488
27 atensor . . . . 491
27.1 Introduction to atensor. . . .491
27.2 Functions and Variables for atensor. . . .492
28 Sums, Products, and Series . . . . 495
28.1 Functions and Variables for Sums and Products. . . .495
28.2 Introduction to Series. . . 499
28.3 Functions and Variables for Series. . . .499
28.4 Introduction to Fourier series. . . .511
28.5 Functions and Variables for Fourier series. . . .511
28.6 Functions and Variables for Poisson series. . . 512
29 Number Theory . . . . 515
29.1 Functions and Variables for Number Theory. . . .515
30 Symmetries . . . . 537
30.1 Introduction to Symmetries. . . 537
30.2 Functions and Variables for Symmetries. . . 537
30.2.1 Changing bases. . . .537
30.2.2 Changing representations. . . .541
30.2.3 Groups and orbits. . . .542
30.2.4 Partitions. . . .545
30.2.5 Polynomials and their roots. . . 546
30.2.6 Resolvents. . . .547
30.2.7 Miscellaneous. . . 553
31 Groups . . . . 555
31.1 Functions and Variables for Groups. . . .555
32 Runtime Environment . . . . 557
32.1 Introduction for Runtime Environment. . . 557
32.2 Interrupts. . . .557
32.3 Functions and Variables for Runtime Environment. . . .557
33 Miscellaneous Options . . . . 565
33.1 Introduction to Miscellaneous Options. . . .565
33.2 Share. . . 565
33.3 Functions and Variables for Miscellaneous Options. . . .565
34.1 Introduction to Rules and Patterns. . . .569
34.2 Functions and Variables for Rules and Patterns. . . .569
35 Sets . . . . 585
35.1 Introduction to Sets. . . .585
35.1.1 Usage. . . .585
35.1.2 Set Member Iteration. . . .587
35.1.3 Authors. . . .588
35.2 Functions and Variables for Sets. . . .588
36 Function Definition . . . . 609
36.1 Introduction to Function Definition. . . .609
36.2 Function. . . 609
36.2.1 Ordinary functions. . . 609
36.2.2 Memoizing Functions. . . .610
36.3 Macros. . . .611
36.4 Functions and Variables for Function Definition. . . .615
37 Program Flow . . . . 641
37.1 Lisp and Maxima. . . 641
37.2 Garbage Collection. . . .642
37.3 Introduction to Program Flow. . . .642
37.4 Functions and Variables for Program Flow. . . .643
38 Debugging . . . . 657
38.1 Source Level Debugging. . . 657
38.2 Keyword Commands. . . 658
38.3 Functions and Variables for Debugging. . . 659
39 alt-display . . . . 665
39.1 Introduction to alt-display. . . .665
39.2 Functions and Variables for alt-display. . . .666
40 asympa . . . . 671
40.1 Introduction to asympa. . . 671
40.2 Functions and variables for asympa. . . .671
41 augmented lagrangian . . . . 673
41.1 Functions and Variables for augmented lagrangian. . . .673
42 Bernstein . . . . 675
42.1 Functions and Variables for Bernstein. . . 675
43.1 Functions and Variables for bitwise. . . 677
44 bode . . . . 681
44.1 Functions and Variables for bode. . . .681
45 celine . . . . 685
45.1 Introduction to celine. . . 685
46 clebsch gordan . . . . 687
46.1 Functions and Variables for clebsch gordan. . . 687
47 cobyla . . . . 689
47.1 Introduction to cobyla. . . .689
47.2 Functions and Variables for cobyla. . . .689
47.3 Examples for cobyla. . . .691
48 combinatorics . . . . 693
48.1 Package combinatorics. . . .693
48.2 Functions and Variables for Combinatorics. . . .693
49 contrib ode . . . . 699
49.1 Introduction to contrib ode. . . .699
49.2 Functions and Variables for contrib ode. . . 701
49.3 Possible improvements to contrib ode. . . .703
49.4 Test cases for contrib ode. . . 704
49.5 References for contrib ode. . . .704
50 descriptive . . . . 705
50.1 Introduction to descriptive. . . 705
50.2 Functions and Variables for data manipulation. . . .707
50.3 Functions and Variables for descriptive statistics. . . .713
50.4 Functions and Variables for statistical graphs. . . .728
51 diag . . . . 739
51.1 Functions and Variables for diag. . . .739
52 distrib . . . . 745
52.1 Introduction to distrib. . . 745
52.2 Functions and Variables for continuous distributions. . . .747
52.3 Functions and Variables for discrete distributions. . . .767
53.1 Introduction to draw. . . 779
53.2 Functions and Variables for draw. . . .780
53.2.1 Scenes. . . 780
53.2.2 Functions. . . 781
53.2.3 Plot options for draw programs. . . .785
53.2.4 Graphics objects. . . 854
53.3 Functions and Variables for pictures. . . .884
53.4 Functions and Variables for worldmap. . . .886
53.4.1 Variables and Functions. . . 886
53.4.2 Graphic objects. . . 891
54 drawdf . . . . 897
54.1 Introduction to drawdf. . . .897
54.2 Functions and Variables for drawdf. . . 897
54.2.1 Functions. . . 897
55 dynamics . . . . 901
55.1 The dynamics package. . . .901
55.2 Graphical analysis of discrete dynamical systems. . . .901
55.3 Visualization with VTK. . . .906
55.3.1 Scene options. . . 908
55.3.2 Scene objects. . . .909
55.3.3 Scene object’s options. . . .910
56 engineering-format . . . . 915
56.1 Functions and Variables for engineering-format. . . 915
56.2 Known Bugs. . . 915
57 ezunits . . . . 917
57.1 Introduction to ezunits. . . .917
57.2 Introduction to physical constants. . . .918
57.3 Functions and Variables for ezunits. . . .920
58 f90 . . . . 935
58.1 Package f90. . . .935
59 finance . . . . 937
59.1 Introduction to finance. . . .937
59.2 Functions and Variables for finance. . . .937
60.1 Introduction to fractals. . . .943
60.2 Definitions for IFS fractals. . . 943
60.3 Definitions for complex fractals. . . .944
60.4 Definitions for Koch snowflakes. . . .945
60.5 Definitions for Peano maps. . . .945
61 ggf . . . . 947
61.1 Functions and Variables for ggf. . . .947
62 graphs . . . . 949
62.1 Introduction to graphs. . . 949
62.2 Functions and Variables for graphs. . . 949
62.2.1 Building graphs. . . 949
62.2.2 Graph properties. . . .955
62.2.3 Modifying graphs. . . .970
62.2.4 Reading and writing to files. . . 972
62.2.5 Visualization. . . .973
63 grobner . . . . 979
63.1 Introduction to grobner. . . 979
63.1.1 Notes on the grobner package. . . .979
63.1.2 Implementations of admissible monomial orders in grobner. .979
63.2 Functions and Variables for grobner. . . 980
63.2.1 Global switches for grobner. . . .980
63.2.2 Simple operators in grobner. . . 981
63.2.3 Other functions in grobner. . . .981
63.2.4 Standard postprocessing of Groebner Bases. . . .983
64 hompack . . . . 987
64.1 Introduction to hompack. . . 987
64.2 Functions and Variables for hompack. . . .987
65 impdiff . . . . 991
65.1 Functions and Variables for impdiff. . . .991
66 interpol . . . . 993
66.1 Introduction to interpol. . . 993
66.2 Functions and Variables for interpol. . . 993
67 lapack . . . . 1001
67.1 Introduction to lapack. . . .1001
67.2 Functions and Variables for lapack. . . 1001
68.1 Introduction to lbfgs. . . 1009
68.2 Functions and Variables for lbfgs. . . .1009
69 lindstedt . . . . 1015
69.1 Functions and Variables for lindstedt. . . .1015
70 linearalgebra . . . . 1017
70.1 Introduction to linearalgebra. . . 1017
70.2 Functions and Variables for linearalgebra. . . 1019
71 lsquares . . . . 1031
71.1 Introduction to lsquares. . . .1031
71.2 Functions and Variables for lsquares. . . .1031
72 minpack . . . . 1041
72.1 Introduction to minpack. . . .1041
72.2 Functions and Variables for minpack. . . 1041
73 makeOrders . . . . 1043
73.1 Functions and Variables for makeOrders. . . .1043
74 mnewton . . . . 1045
74.1 Introduction to mnewton. . . .1045
74.2 Functions and Variables for mnewton. . . .1045
75 numericalio . . . . 1047
75.1 Introduction to numericalio. . . 1047
75.1.1 Plain-text input and output. . . 1047
75.1.2 Separator flag values for input. . . .1047
75.1.3 Separator flag values for output. . . 1047
75.1.4 Binary floating-point input and output. . . 1048
75.2 Functions and Variables for plain-text input and output. . . . 1048
75.3 Functions and Variables for binary input and output. . . .1050
76 odepack . . . . 1053
76.1 Introduction to ODEPACK. . . 1053
76.1.1 Getting Started with ODEPACK. . . 1053
76.2 Functions and Variables for odepack. . . .1054
77 operatingsystem . . . . 1057
77.1 Introduction to operatingsystem. . . .1057
77.2 Directory operations. . . 1057
77.3 File operations. . . .1057
77.4 Environment operations. . . .1057
78.1 Functions and Variables for opsubst. . . 1059
79 orthopoly . . . . 1061
79.1 Introduction to orthogonal polynomials. . . .1061
79.1.1 Getting Started with orthopoly. . . .1061
79.1.2 Limitations. . . 1063
79.1.3 Floating point Evaluation. . . 1065
79.1.4 Graphics andorthopoly. . . 1066
79.1.5 Miscellaneous Functions. . . .1067
79.1.6 Algorithms. . . .1068
79.2 Functions and Variables for orthogonal polynomials. . . .1068
80 pytranslate . . . . 1073
80.1 Introduction to pytranslate. . . .1073
80.1.1 Tests for pytranslate. . . 1074
80.2 Functions in pytranslate. . . .1074
80.3 Extending pytranslate. . . .1075
81 ratpow . . . . 1079
81.1 Functions and Variables for ratpow. . . .1079
82 romberg . . . . 1081
82.1 Functions and Variables for romberg. . . .1081
83 simplex . . . . 1085
83.1 Introduction to simplex. . . 1085
83.1.1 Tests for simplex. . . .1085
83.1.1.1 klee minty. . . 1085
83.1.1.2 NETLIB. . . 1085
83.2 Functions and Variables for simplex. . . 1086
84 simplification . . . . 1089
84.1 Introduction to simplification. . . .1089
84.2 Package absimp. . . 1089
84.3 Package facexp. . . .1089
84.4 Package functs. . . .1091
84.5 Package ineq. . . .1094
84.6 Package rducon. . . 1096
84.7 Package scifac. . . .1096
85 solve rec . . . . 1099
85.1 Introduction to solve rec. . . 1099
85.2 Functions and Variables for solve rec. . . .1099
86.1 Introduction to stats. . . 1105
86.2 Functions and Variables for inference result. . . 1105
86.3 Functions and Variables for stats. . . .1107
86.4 Functions and Variables for special distributions. . . .1122
87 stirling . . . . 1123
87.1 Functions and Variables for stirling. . . .1123
88 stringproc . . . . 1125
88.1 Introduction to String Processing. . . .1125
88.2 Input and Output. . . .1126
88.3 Characters. . . .1132
88.4 String Processing. . . 1137
88.5 Octets and Utilities for Cryptography. . . 1143
89 to poly solve . . . . 1149
89.1 Functions and Variables for to poly solve. . . .1149
90 unit . . . . 1169
90.1 Introduction to Units. . . 1169
90.2 Functions and Variables for Units. . . 1170
91 wrstcse . . . . 1179
91.1 Introduction to wrstcse. . . .1179
91.2 Functions and Variables for wrstcse. . . .1179
92 zeilberger . . . . 1183
92.1 Introduction to zeilberger. . . 1183
92.1.1 The indefinite summation problem. . . .1183
92.1.2 The definite summation problem. . . 1183
92.1.3 Verbosity levels. . . 1183
92.2 Functions and Variables for zeilberger. . . 1184
92.3 General global variables. . . .1185
92.4 Variables related to the modular test. . . .1186
93 Error and warning messages . . . . 1187
93.1 Error messages. . . .1187
93.1.1 apply: no such"list"element. . . .1187
93.1.2 argument must be a non-atomic expression. . . 1187
93.1.3 assignment: cannot assign to <function name>. . . 1187
93.1.4 expt: undefined: 0 to a negative exponent.. . . .1187
93.1.5 incorrect syntax: , is not a prefix operator. . . 1187
93.1.6 incorrect syntax: Illegal use of delimiter ). . . .1187
93.1.7 loadfile: failed to load<filename>. . . .1188
93.1.9 Only symbols can be bound. . . 1188
93.1.10 operators of arguments must all be the same. . . .1188
93.1.11 Out of memory. . . 1188
93.1.12 part: fell off the end. . . .1189
93.1.13 undefined variable (draw or plot). . . .1189
93.1.14 VTK is not installed, which is required for Scene. . . 1189
93.2 Warning messages. . . .1189
93.2.1 Encountered undefined variable<x>in translation . . . 1190
93.2.2 Rat: replaced<x>by <y> = <z>. . . 1190
94 Command-line options . . . . 1191
94.1 Command line options. . . 1191
Appendix A Function and Variable Index . . . 1193
1 Introduction to Maxima
Start Maxima with the command "maxima". Maxima will display version information and a prompt. End each Maxima command with a semicolon. End the session with the command "quit();". Here’s a sample session:
[wfs@chromium]$ maxima
Maxima 5.9.1 http://maxima.sourceforge.net Using Lisp CMU Common Lisp 19a
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
This is a development version of Maxima. The function bug_report() provides bug reporting information.
(%i1) factor(10!);
8 4 2
(%o1) 2 3 5 7
(%i2) expand ((x + y)^6);
6 5 2 4 3 3 4 2 5 6
(%o2) y + 6 x y + 15 x y + 20 x y + 15 x y + 6 x y + x (%i3) factor (x^6 - 1);
2 2
(%o3) (x - 1) (x + 1) (x - x + 1) (x + x + 1) (%i4) quit();
[wfs@chromium]$
Maxima can search the info pages. Use the describe command to show information about the command or all the commands and variables containing a string. The question mark ?(exact search) and double question mark?? (inexact search) are abbreviations for describe:
(%i1) ?? integ
0: Functions and Variables for Elliptic Integrals 1: Functions and Variables for Integration
2: Introduction to Elliptic Functions and Integrals 3: Introduction to Integration
4: askinteger (Functions and Variables for Simplification) 5: integerp (Functions and Variables for Miscellaneous Options) 6: integer_partitions (Functions and Variables for Sets)
7: integrate (Functions and Variables for Integration)
8: integrate_use_rootsof (Functions and Variables for Integration) 9: integration_constant_counter (Functions and Variables for
Integration)
10: nonnegintegerp (Functions and Variables for linearalgebra) Enter space-separated numbers, ‘all' or ‘none': 5 4
-- Function: integerp (<expr>)
Returns ‘true' if <expr> is a literal numeric integer, otherwise
‘false'.
‘integerp' returns false if its argument is a symbol, even if the argument is declared integer.
Examples:
(%i1) integerp (0);
(%o1) true
(%i2) integerp (1);
(%o2) true
(%i3) integerp (-17);
(%o3) true
(%i4) integerp (0.0);
(%o4) false
(%i5) integerp (1.0);
(%o5) false
(%i6) integerp (%pi);
(%o6) false
(%i7) integerp (n);
(%o7) false
(%i8) declare (n, integer);
(%o8) done
(%i9) integerp (n);
(%o9) false
-- Function: askinteger (<expr>, integer) -- Function: askinteger (<expr>)
-- Function: askinteger (<expr>, even) -- Function: askinteger (<expr>, odd)
‘askinteger (<expr>, integer)' attempts to determine from the
‘assume' database whether <expr> is an integer. ‘askinteger' prompts the user if it cannot tell otherwise, and attempt to install the information in the database if possible. ‘askinteger (<expr>)' is equivalent to ‘askinteger (<expr>, integer)'.
‘askinteger (<expr>, even)' and ‘askinteger (<expr>, odd)'
likewise attempt to determine if <expr> is an even integer or odd integer, respectively.
(%o1) true
To use a result in later calculations, you can assign it to a variable or refer to it by its automatically supplied label. In addition,%refers to the most recent calculated result:
(%i1) u: expand ((x + y)^6);
6 5 2 4 3 3 4 2 5 6
(%o1) y + 6 x y + 15 x y + 20 x y + 15 x y + 6 x y + x (%i2) diff (u, x);
5 4 2 3 3 2 4 5
(%o2) 6 y + 30 x y + 60 x y + 60 x y + 30 x y + 6 x (%i3) factor (%o2);
5
(%o3) 6 (y + x)
Maxima knows about complex numbers and numerical constants:
(%i1) cos(%pi);
(%o1) - 1
(%i2) exp(%i*%pi);
(%o2) - 1
Maxima can do differential and integral calculus:
(%i1) u: expand ((x + y)^6);
6 5 2 4 3 3 4 2 5 6
(%o1) y + 6 x y + 15 x y + 20 x y + 15 x y + 6 x y + x (%i2) diff (%, x);
5 4 2 3 3 2 4 5
(%o2) 6 y + 30 x y + 60 x y + 60 x y + 30 x y + 6 x (%i3) integrate (1/(1 + x^3), x);
2 x - 1
2 atan(---)
log(x - x + 1) sqrt(3) log(x + 1) (%o3) - --- + --- + ---
6 sqrt(3) 3
Maxima can solve linear systems and cubic equations:
(%i1) linsolve ([3*x + 4*y = 7, 2*x + a*y = 13], [x, y]);
7 a - 52 25
(%o1) [x = ---, y = ---]
3 a - 8 3 a - 8 (%i2) solve (x^3 - 3*x^2 + 5*x = 15, x);
(%o2) [x = - sqrt(5) %i, x = sqrt(5) %i, x = 3]
Maxima can solve nonlinear sets of equations. Note that if you don’t want a result printed, you can finish your command with$ instead of;.
(%i1) eq_1: x^2 + 3*x*y + y^2 = 0$
(%i2) eq_2: 3*x + y = 1$
(%i3) solve ([eq_1, eq_2]);
3 sqrt(5) + 7 sqrt(5) + 3 (%o3) [[y = - ---, x = ---],
2 2
3 sqrt(5) - 7 sqrt(5) - 3 [y = ---, x = - ---]]
2 2
Maxima can generate plots of one or more functions:
(%i1) plot2d (sin(x)/x, [x, -20, 20])$
sin(x)/x
x -0.2
0 0.2 0.4 0.6 0.8 1
-20 -15 -10 -5 0 5 10 15 20
(%i2) plot2d ([atan(x), erf(x), tanh(x)], [x, -5, 5], [y, -1.5, 2])$
x
atan(x) erf(x) tanh(x)
-1.5 -1 -0.5 0 0.5 1 1.5 2
-4 -2 0 2 4
(%i3) plot3d (sin(sqrt(x^2 + y^2))/sqrt(x^2 + y^2), [x, -12, 12], [y, -12, 12])$
-10 -5
0 5
10 -10
-5 0
5 10 -0.4
-0.2 0 0.2 0.4 0.6 0.8 1
sin(sqrt(y^2+x^2))/sqrt(y^2+x^2)
x
y z
2 Bug Detection and Reporting
2.1 Functions and Variables for Bug Detection and Reporting
[Function]
run_testsuite ([options])
Run the Maxima test suite. Tests producing the desired answer are considered
“passes,” as are tests that do not produce the desired answer, but are marked as known bugs.
run_testsuitetakes the following optional keyword arguments display_all
Display all tests. Normally, the tests are not displayed, unless the test fails. (Defaults tofalse).
display_known_bugs
Displays tests that are marked as known bugs. (Default isfalse).
tests This is a single test or a list of tests that should be run. Each test can be specified by either a string or a symbol. By default, all tests are run.
The complete set of tests is specified bytestsuite_files.
time Display time information. If true, the time taken for each test file is displayed. If all, the time for each individual test is shown if display_
allistrue. The default is false, so no timing information is shown.
share_tests
Load additional tests for the share directory. If true, these additional tests are run as a part of the testsuite. Iffalse, no tests from theshare directory are run. If only, only the tests from the share directory are run. Of course, the actual set of test that are run can be controlled by thetestsoption. The default is false.
For example run_testsuite(display_known_bugs = true, tests=[rtest5]) runs just testrtest5and displays the test that are marked as known bugs.
run_testsuite(display_all = true, tests=["rtest1", rtest1a]) will run tests rtest1and rtest2, and displays each test.
run_testsuite changes the Maxima environment. Typically a test script executes kill to establish a known environment (namely one without user-defined functions and variables) and then defines functions and variables appropriate to the test.
run_testsuitereturns done.
[Option variable]
testsuite_files
testsuite_filesis the set of tests to be run byrun_testsuite. It is a list of names of the files containing the tests to run. If some of the tests in a file are known to fail, then instead of listing the name of the file, a list containing the file name and the test numbers that fail is used.
For example, this is a part of the default set of tests:
["rtest13s", ["rtest14", 57, 63]]
This specifies the testsuite consists of the files"rtest13s"and"rtest14", but"rtest14"
contains two tests that are known to fail: 57 and 63.
[Option variable]
share_testsuite_files
share_testsuite_files is the set of tests from thesharedirectory that is run as a part of the test suite byrun_testsuite..
[Function]
bug_report ()
Prints out Maxima and Lisp version numbers, and gives a link to the Maxima project bug report web page. The version information is the same as reported bybuild_info.
When a bug is reported, it is helpful to copy the Maxima and Lisp version information into the bug report.
bug_report returns an empty string"".
[Function]
build_info ()
Returns a summary of the parameters of the Maxima build, as a Maxima structure (defined by defstruct). The fields of the structure are: version,timestamp,host, lisp_name, andlisp_version. When the pretty-printer is enabled (viadisplay2d), the structure is displayed as a short table.
See also bug_report.
Examples:
(%i1) build_info ();
(%o1)
Maxima version: "5.36.1"
Maxima build date: "2015-06-02 11:26:48"
Host type: "x86_64-unknown-linux-gnu"
Lisp implementation type: "GNU Common Lisp (GCL)"
Lisp implementation version: "GCL 2.6.12"
(%i2) x : build_info ()$
(%i3) x@version;
(%o3) 5.36.1
(%i4) x@timestamp;
(%o4) 2015-06-02 11:26:48
(%i5) x@host;
(%o5) x86_64-unknown-linux-gnu
(%i6) x@lisp_name;
(%o6) GNU Common Lisp (GCL)
(%i7) x@lisp_version;
(%o7) GCL 2.6.12
(%i8) x;
(%o8)
Maxima version: "5.36.1"
Maxima build date: "2015-06-02 11:26:48"
Host type: "x86_64-unknown-linux-gnu"
Lisp implementation type: "GNU Common Lisp (GCL)"
Lisp implementation version: "GCL 2.6.12"
The Maxima version string can (here 5.36.1) can look very different:
(%i1) build_info();
(%o1)
Maxima version: "branch_5_37_base_331_g8322940_dirty"
Maxima build date: "2016-01-01 15:37:35"
Host type: "x86_64-unknown-linux-gnu"
Lisp implementation type: "CLISP"
Lisp implementation version: "2.49 (2010-07-07) (built 3605577779) (memory 3660647857)"
In that case, Maxima was not build from a released sourcecode, but directly from the GIT-checkout of the sourcecode. In the example, the checkout is 331 commits after the latest GIT tag (usually a Maxima (major) release (5.37 in our example)) and the abbreviated commit hash of the last commit was "8322940".
Front-ends for maxima can add information about currently being used by setting the variablesmaxima_frontend andmaxima_frontend_versionaccordingly.
3 Help
3.1 Documentation
The Maxima on-line user’s manual can be viewed in different forms. From the Maxima interactive prompt, the user’s manual is viewed as plain text by the ?command (i.e., the describe function). The user’s manual is viewed as info hypertext by the info viewer program and as a web page by any ordinary web browser.
example displays examples for many Maxima functions. For example, (%i1) example (integrate);
yields
(%i2) test(f):=block([u],u:integrate(f,x),ratsimp(f-diff(u,x))) (%o2) test(f) := block([u], u : integrate(f, x),
ratsimp(f - diff(u, x))) (%i3) test(sin(x))
(%o3) 0
(%i4) test(1/(x+1))
(%o4) 0
(%i5) test(1/(x^2+1))
(%o5) 0
and additional output.
3.2 Functions and Variables for Help
[Function]
apropos (name)
Searches for Maxima names which havenameappearing anywhere within them;name must be a string or symbol. Thus, apropos (exp) returns a list of all the flags and functions which have exp as part of their names, such as expand, exp, and exponentialize. So, if you can only remember part of the name of a Maxima com- mand or variable, you can use this command to find the rest of the name. Similarly, you can type apropos (tr_) to find a list of many of the switches relating to the translator, most of which begin withtr_.
apropos("")returns a list with all Maxima names.
apropos returns the empty list[], if no name is found.
Example:
Show all Maxima symbols which have gammain the name:
(%i1) apropos("gamma");
(%o1) [%gamma, Gamma, gamma_expand, gammalim, makegamma,
prefer_gamma_incomplete, gamma, gamma-incomplete, gamma_incomplete, gamma_incomplete_generalized, gamma_incomplete_generalized_regularized, gamma_incomplete_lower, gamma_incomplete_regularized, log_gamma]
The same example, using the symbol gamma, rather than the string:
(%i2) apropos(gamma);
(%o2) [%gamma, Gamma, gamma_expand, gammalim, makegamma,
prefer_gamma_incomplete, gamma, gamma-incomplete, gamma_incomplete, gamma_incomplete_generalized, gamma_incomplete_generalized_regularized, gamma_incomplete_lower, gamma_incomplete_regularized, log_gamma]
The number of symbols in the current Maxima session. This will vary.
(%i3) length(apropos(""));
(%o3) 2338
[Function]
demo (filename)
Evaluates Maxima expressions infilename and displays the results. demopauses after evaluating each expression and continues after the user enters a carriage return. (If running in Xmaxima, demo may need to see a semicolon ; followed by a carriage return.)
demo searches the list of directories file_search_demo to find filename. If the file has the suffix dem, the suffix may be omitted. See alsofile_search.
demo evaluates its argument. demo returns the name of the demonstration file.
Example:
(%i1) demo ("disol");
batching /home/wfs/maxima/share/simplification/disol.dem At the _ prompt, type ';' followed by enter to get next demo (%i2) load("disol")
_
(%i3) exp1 : a (e (g + f) + b (d + c)) (%o3) a (e (g + f) + b (d + c)) _
(%i4) disolate(exp1, a, b, e)
(%t4) d + c
(%t5) g + f
(%o5) a (%t5 e + %t4 b)
_
[Function]
describe
describe (string)
describe (string, exact) describe (string, inexact)
describe(string)is equivalent todescribe(string, exact).
describe(string, exact)finds an item with title equal (case-insensitive) tostring, if there is any such item.
describe(string, inexact)finds all documented items which containstringin their titles. If there is more than one such item, Maxima asks the user to select an item or items to display.
At the interactive prompt, ? foo (with a space between ? and foo) is equivalent to describe("foo", exact), and ?? foo is equivalent todescribe("foo", inexact).
describe("", inexact) yields a list of all topics documented in the on-line manual.
describe quotes its argument. describe returns true if some documentation is found, otherwise false.
See also Section 3.1 [Documentation], page 11.
Example:
(%i1) ?? integ
0: Functions and Variables for Elliptic Integrals 1: Functions and Variables for Integration
2: Introduction to Elliptic Functions and Integrals 3: Introduction to Integration
4: askinteger (Functions and Variables for Simplification) 5: integerp (Functions and Variables for Miscellaneous Options) 6: integer_partitions (Functions and Variables for Sets)
7: integrate (Functions and Variables for Integration) 8: integrate_use_rootsof (Functions and Variables for
Integration)
9: integration_constant_counter (Functions and Variables for Integration)
10: nonnegintegerp (Functions and Variables for linearalgebra) Enter space-separated numbers, ‘all' or ‘none': 7 8
-- Function: integrate (<expr>, <x>)
-- Function: integrate (<expr>, <x>, <a>, <b>)
Attempts to symbolically compute the integral of <expr> with respect to <x>. ‘integrate (<expr>, <x>)' is an indefinite integral, while ‘integrate (<expr>, <x>, <a>, <b>)' is a definite integral, [...]
-- Option variable: integrate_use_rootsof Default value: ‘false'
When ‘integrate_use_rootsof' is ‘true' and the denominator of a rational function cannot be factored, ‘integrate' returns the integral in a form which is a sum over the roots (not yet known) of the denominator.
[...]
In this example, items 7 and 8 were selected (output is shortened as indicated by [...]). All or none of the items could have been selected by entering allor none, which can be abbreviated aorn, respectively.
[Function]
example
example (topic) example ()
example (topic)displays some examples of topic, which is a symbol or a string. To get examples for operators like if,do, orlambdathe argument must be a string, e.g.
example ("do"). example is not case sensitive. Most topics are function names.
example ()returns the list of all recognized topics.
The name of the file containing the examples is given by the global option variable manual_demo, which defaults to"manual.demo".
examplequotes its argument. examplereturnsdoneunless no examples are found or there is no argument, in which case examplereturns the list of all recognized topics.
Examples:
(%i1) example(append);
(%i2) append([y+x,0,-3.2],[2.5e+20,x])
(%o2) [y + x, 0, - 3.2, 2.5e+20, x]
(%o2) done
(%i3) example("lambda");
(%i4) lambda([x,y,z],x^2+y^2+z^2)
2 2 2
(%o4) lambda([x, y, z], x + y + z ) (%i5) %(1,2,a)
2
(%o5) a + 5
(%i6) 1+2+a
(%o6) a + 3
(%o6) done
[Option variable]
manual_demo
Default value: "manual.demo"
manual_demo specifies the name of the file containing the examples for the function example. See example.
4 Command Line
4.1 Introduction to Command Line
4.2 Functions and Variables for Command Line
[System variable]
__
__ is the input expression currently being evaluated. That is, while an input expres- sion expr is being evaluated,__ isexpr.
__ is assigned the input expression before the input is simplified or evaluated. How- ever, the value of__ is simplified (but not evaluated) when it is displayed.
__ is recognized by batch and load. In a file processed by batch, __ has the same meaning as at the interactive prompt. In a file processed by load,__is bound to the input expression most recently entered at the interactive prompt or in a batch file;
__ is not bound to the input expressions in the file being processed. In particular, when load (filename) is called from the interactive prompt, __ is bound to load (filename)while the file is being processed.
See also _and %.
Examples:
(%i1) print ("I was called as", __);
I was called as print(I was called as, __) (%o1) print(I was called as, __) (%i2) foo (__);
(%o2) foo(foo(__))
(%i3) g (x) := (print ("Current input expression =", __), 0);
(%o3) g(x) := (print("Current input expression =", __), 0) (%i4) [aa : 1, bb : 2, cc : 3];
(%o4) [1, 2, 3]
(%i5) (aa + bb + cc)/(dd + ee + g(x));
cc + bb + aa Current input expression = ---
g(x) + ee + dd 6
(%o5) ---
ee + dd
[System variable]
_
_is the most recent input expression (e.g., %i1,%i2,%i3, . . . ).
_is assigned the input expression before the input is simplified or evaluated. However, the value of_is simplified (but not evaluated) when it is displayed.
_ is recognized by batch and load. In a file processed by batch, _ has the same meaning as at the interactive prompt. In a file processed by load,_is bound to the input expression most recently evaluated at the interactive prompt or in a batch file;
_is not bound to the input expressions in the file being processed.
See also __ and %.
Examples:
(%i1) 13 + 29;
(%o1) 42
(%i2) :lisp $_
((MPLUS) 13 29) (%i2) _;
(%o2) 42
(%i3) sin (%pi/2);
(%o3) 1
(%i4) :lisp $_
((%SIN) ((MQUOTIENT) $%PI 2)) (%i4) _;
(%o4) 1
(%i5) a: 13$
(%i6) b: 29$
(%i7) a + b;
(%o7) 42
(%i8) :lisp $_
((MPLUS) $A $B) (%i8) _;
(%o8) b + a
(%i9) a + b;
(%o9) 42
(%i10) ev (_);
(%o10) 42
[System variable]
%
% is the output expression (e.g., %o1, %o2, %o3, . . . ) most recently computed by Maxima, whether or not it was displayed.
% is recognized by batch and load. In a file processed by batch, % has the same meaning as at the interactive prompt. In a file processed by load,%is bound to the output expression most recently computed at the interactive prompt or in a batch file; %is not bound to output expressions in the file being processed.
See also _,%%, and %th.
[System variable]
%%
In compound statements, namelyblock,lambda, or(s_1, ..., s_n),%%is the value of the previous statement.
At the first statement in a compound statement, or outside of a compound statement,
%% is undefined.
%%is recognized bybatchandload, and it has the same meaning as at the interactive prompt.
See also %.
Examples:
The following two examples yield the same result.
(%i1) block (integrate (x^5, x), ev (%%, x=2) - ev (%%, x=1));
21
(%o1) --
2
(%i2) block ([prev], prev: integrate (x^5, x), ev (prev, x=2) - ev (prev, x=1));
21
(%o2) --
2
A compound statement may comprise other compound statements. Whether a state- ment be simple or compound, %% is the value of the previous statement.
(%i3) block (block (a^n, %%*42), %%/6);
n
(%o3) 7 a
Within a compound statement, the value of %%may be inspected at a break prompt, which is opened by executing the break function. For example, entering %%; in the following example yields42.
(%i4) block (a: 42, break ())$
Entering a Maxima break point. Type 'exit;' to resume.
_%%;
42 _
[Function]
%th (i)
The value of the i’th previous output expression. That is, if the next expression to be computed is the n’th output,%th (m)is the (n- m)’th output.
%this recognized bybatchand load. In a file processed bybatch,%thhas the same meaning as at the interactive prompt. In a file processed byload,%threfers to output expressions most recently computed at the interactive prompt or in a batch file; %th does not refer to output expressions in the file being processed.
See also %and %%.
Example:
%th is useful in batch files or for referring to a group of output expressions. This example setssto the sum of the last five output expressions.
(%i1) 1;2;3;4;5;
(%o1) 1
(%o2) 2
(%o3) 3
(%o4) 4
(%o5) 5
(%i6) block (s: 0, for i:1 thru 5 do s: s + %th(i), s);
(%o6) 15
[Special symbol]
?
As prefix to a function or variable name, ? signifies that the name is a Lisp name, not a Maxima name. For example, ?round signifies the Lisp function ROUND. See Section 37.1 [Lisp and Maxima], page 641, for more on this point.
The notation ? word (a question mark followed a word, separated by whitespace) is equivalent todescribe("word"). The question mark must occur at the beginning of an input line; otherwise it is not recognized as a request for documentation. See also describe.
[Special symbol]
??
The notation ?? word(??followed a word, separated by whitespace) is equivalent to describe("word", inexact). The question mark must occur at the beginning of an input line; otherwise it is not recognized as a request for documentation. See also describe.
[Input terminator]
$
The dollar sign $terminates an input expression, and the most recent output% and an output label, e.g. %o1, are assigned the result, but the result is not displayed.
See also ;.
Example:
(%i1) 1 + 2 + 3 $ (%i2) %;
(%o2) 6
(%i3) %o1;
(%o3) 6
[Input terminator]
;
The semicolon;terminates an input expression, and the resulting output is displayed.
See also $.
Example:
(%i1) 1 + 2 + 3;
(%o1) 6
[Option variable]
inchar
Default value: %i
inchar is the prefix of the labels of expressions entered by the user. Maxima auto- matically constructs a label for each input expression by concatenating inchar and linenum.
inchar may be assigned any string or symbol, not necessarily a single character.
Because Maxima internally takes into account only the first char of the prefix, the prefixesinchar,outchar, andlinecharshould have a different first char. Otherwise some commands likekill(inlabels) do not work as expected.
See also labels.
Example:
(%i1) inchar: "input";
(%o1) input
(input2) expand((a+b)^3);
3 2 2 3
(%o2) b + 3 a b + 3 a b + a
[System variable]
infolists
Default value: []
infolists is a list of the names of all of the information lists in Maxima. These are:
labels All bound%i,%o, and %t labels.
values All bound atoms which are user variables, not Maxima options or switches, created by: or::or functional binding.
functions
All user-defined functions, created by:=ordefine.
arrays All arrays,hashed arraysand memoizing functions.
macros All user-defined macro functions, created by::=.
myoptions
All options ever reset by the user (whether or not they are later reset to their default values).
rules All user-defined pattern matching and simplification rules, created by tellsimp,tellsimpafter,defmatch, ordefrule.
aliases All atoms which have an user-defined alias, created by the alias, ordergreat, orderless functions or by declaring the atom as a noun withdeclare.
dependencies
All atoms which have functional dependencies, created by thedepends, dependencies, orgradeffunctions.
gradefs All functions which have user-defined derivatives, created by thegradef function.
props All atoms which have any property other than those mentioned above, such as properties established byatvalueormatchdeclare, etc., as well as properties established in thedeclarefunction.
structures
All structs defined usingdefstruct.
let_rule_packages
All user-defined let rule packages plus the special package default_
let_rule_package. (default_let_rule_package is the name of the rule package used when one is not explicitly set by the user.)
[Function]
kill
kill(a_1, . . . , a_n) kill(labels)
kill(inlabels, outlabels, linelabels) kill(n)
kill([m, n])
kill(values, functions, arrays, . . .) kill(all)
kill(allbut (a_1, . . . , a_n))
Removes all bindings (value, function, array, or rule) from the arguments a 1, . . . , a n. An argument a k may be a symbol or a single array element. When a k is a single array element, killunbinds that element without affecting any other elements of the array.
Several special arguments are recognized. Different kinds of arguments may be com- bined, e.g., kill (inlabels, functions, allbut (foo, bar)).
kill (labels)unbinds all input, output, and intermediate expression labels created so far. kill (inlabels)unbinds only input labels which begin with the current value ofinchar. Likewise,kill (outlabels)unbinds only output labels which begin with the current value of outchar, and kill (linelabels) unbinds only intermediate expression labels which begin with the current value oflinechar.
kill (n), wheren is an integer, unbinds then most recent input and output labels.
kill ([m,n]) unbinds input and output labels mthrough n.
kill (infolist), where infolist is any item in infolists (such as values, functions, orarrays) unbinds all items in infolist. See alsoinfolists.
kill (all) unbinds all items on all infolists. kill (all) does not reset global vari- ables to their default values; see reseton this point.
kill (allbut (a_1, ..., a_n))unbinds all items on all infolists except fora 1, . . . , a n. kill (allbut (infolist)) unbinds all items except for the ones on infolist, where infolistis values,functions,arrays, etc.
The memory taken up by a bound property is not released until all symbols are unbound from it. In particular, to release the memory taken up by the value of a symbol, one unbinds the output label which shows the bound value, as well as unbinding the symbol itself.
kill quotes its arguments. The quote-quote operator'' defeats quotation.
kill (symbol)unbinds all properties ofsymbol. In contrast, the functionsremvalue, remfunction, remarray, and remrule unbind a specific property. Note that facts declared by assumedon’t require a symbol they apply to, therefore aren’t stored as properties of symbols and therefore aren’t affected bykill.
kill always returns done, even if an argument has no binding.
[Function]
labels (symbol)
Returns the list of input, output, or intermediate expression labels which begin with symbol. Typicallysymbol is the value ofinchar,outchar, or linechar. If no labels begin with symbol,labelsreturns an empty list.
By default, Maxima displays the result of each user input expression, giving the result an output label. The output display is suppressed by terminating the input with $ (dollar sign) instead of ; (semicolon). An output label is constructed and bound to the result, but not displayed, and the label may be referenced in the same way as displayed output labels. See also %,%%, and %th.
Intermediate expression labels can be generated by some functions. The option vari- ableprogrammodecontrols whethersolveand some other functions generate interme- diate expression labels instead of returning a list of expressions. Some other functions, such asldisplay, always generate intermediate expression labels.
See also inchar,outchar,linechar, andinfolists.
[System variable]
labels
The variable labelsis the list of input, output, and intermediate expression labels, including all previous labels if inchar,outchar, orlinecharwere redefined.
[Option variable]
linechar
Default value: %t
linechar is the prefix of the labels of intermediate expressions generated by Max- ima. Maxima constructs a label for each intermediate expression (if displayed) by concatenating linecharand linenum.
linechar may be assigned any string or symbol, not necessarily a single character.
Because Maxima internally takes into account only the first char of the prefix, the prefixesinchar,outchar, andlinecharshould have a different first char. Otherwise some commands likekill(inlabels) do not work as expected.
Intermediate expressions might or might not be displayed. See programmode and labels.
[System variable]
linenum
The line number of the current pair of input and output expressions.
[System variable]
myoptions
Default value: []
myoptions is the list of all options ever reset by the user, whether or not they get reset to their default value.
[Option variable]
nolabels
Default value: false
When nolabelsis true, input and output result labels (%iand %o, respectively) are displayed, but the labels are not bound to results, and the labels are not appended to thelabelslist. Since labels are not bound to results, garbage collection can recover the memory taken up by the results.
Otherwise input and output result labels are bound to results, and the labels are appended to thelabelslist.
Intermediate expression labels (%t) are not affected bynolabels; whethernolabels is true or false, intermediate expression labels are bound and appended to the labelslist.
See also batch,load, and labels.
[Option variable]
optionset
Default value: false
When optionset is true, Maxima prints out a message whenever a Maxima option is reset. This is useful if the user is doubtful of the spelling of some option and wants to make sure that the variable he assigned a value to was truly an option variable.
Example:
(%i1) optionset:true;
assignment: assigning to option optionset
(%o1) true
(%i2) gamma_expand:true;
assignment: assigning to option gamma_expand
(%o2) true
[Option variable]
outchar
Default value: %o
outcharis the prefix of the labels of expressions computed by Maxima. Maxima auto- matically constructs a label for each computed expression by concatenating outchar and linenum.
outchar may be assigned any string or symbol, not necessarily a single character.
Because Maxima internally takes into account only the first char of the prefix, the prefixesinchar,outcharandlinecharshould have a different first char. Otherwise some commands likekill(inlabels) do not work as expected.
See also labels.
Example:
(%i1) outchar: "output";
(output1) output
(%i2) expand((a+b)^3);
3 2 2 3
(output2) b + 3 a b + 3 a b + a
[Function]
playback
playback () playback (n) playback ([m, n]) playback ([m]) playback (input) playback (slow) playback (time) playback (grind)
Displays input, output, and intermediate expressions, without recomputing them.
playback only displays the expressions bound to labels; any other output (such as text printed by print or describe, or error messages) is not displayed. See also labels.
playback quotes its arguments. The quote-quote operator '' defeats quotation.
playbackalways returns done.
playback ()(with no arguments) displays all input, output, and intermediate expres- sions generated so far. An output expression is displayed even if it was suppressed by the$terminator when it was originally computed.
playback (n)displays the most recent nexpressions. Each input, output, and inter- mediate expression counts as one.
playback ([m,n]) displays input, output, and intermediate expressions with num- bers from mthrough n, inclusive.
playback ([m]) is equivalent to playback ([m,m]); this usually prints one pair of input and output expressions.
playback (input) displays all input expressions generated so far.
playback (slow) pauses between expressions and waits for the user to press enter.
This behavior is similar to demo. playback (slow) is useful in conjunction with save orstringoutwhen creating a secondary-storage file in order to pick out useful expressions.
playback (time)displays the computation time for each expression.
playback (grind) displays input expressions in the same format as the grindfunc- tion. Output expressions are not affected by thegrind option. Seegrind.
Arguments may be combined, e.g., playback ([5, 10], grind, time, slow).
[Option variable]
prompt
Default value: _
promptis the prompt symbol of thedemo function, playback (slow)mode, and the Maxima break loop (as invoked by break).
[Function]
quit ()
Terminates the Maxima session. Note that the function must be invoked as quit();
orquit()$, notquit by itself.
To stop a lengthy computation, typecontrol-C. The default action is to return to the Maxima prompt. If *debugger-hook* is nil, control-C opens the Lisp debugger.
See also Chapter 38 [Debugging], page 657.
[Function]
read (expr_1, . . . , expr_n)
Prints expr 1, . . . , expr n, then reads one expression from the console and returns the evaluated expression. The expression is terminated with a semicolon ; or dollar sign $.
See also readonly Example:
(%i1) foo: 42$
(%i2) foo: read ("foo is", foo, " -- enter new value.")$
foo is 42 -- enter new value.
(a+b)^3;
(%i3) foo;
3
(%o3) (b + a)
[Function]
readonly (expr_1, . . . , expr_n)
Printsexpr 1, . . . ,expr n, then reads one expression from the console and returns the expression (without evaluation). The expression is terminated with a ; (semicolon) or$(dollar sign).
See also read.
Examples:
(%i1) aa: 7$
(%i2) foo: readonly ("Enter an expression:");
Enter an expression:
2^aa;
aa
(%o2) 2
(%i3) foo: read ("Enter an expression:");
Enter an expression:
2^aa;
(%o3) 128
[Function]
reset ()
Resets many global variables and options, and some other variables, to their default values.
reset processes the variables on the Lisp list *variable-initial-values*. The Lisp macrodefmvarputs variables on this list (among other actions). Many, but not all, global variables and options are defined by defmvar, and some variables defined by defmvar are not global variables or options.
[Option variable]
showtime
Default value: false
Whenshowtimeistrue, the computation time and elapsed time is printed with each output expression.
The computation time is always recorded, so time and playback can display the computation time even when showtimeis false.
See also timer.
[Function]
to_lisp ()
Enters the Lisp system under Maxima. (to-maxima)returns to Maxima.
Example:
Define a function and enter the Lisp system under Maxima. The definition is inspected on the property list, then the function definition is extracted, factored and stored in the variable$result. The variable can be used in Maxima after returning to Maxima.
(%i1) f(x):=x^2+x;
2
(%o1) f(x) := x + x
(%i2) to_lisp();
Type (to-maxima) to restart, ($quit) to quit Maxima.
MAXIMA> (symbol-plist '$f)
(MPROPS (NIL MEXPR ((LAMBDA) ((MLIST) $X)
((MPLUS) ((MEXPT) $X 2) $X)))) MAXIMA> (setq $result ($factor (caddr (mget '$f 'mexpr)))) ((MTIMES SIMP FACTORED) $X ((MPLUS SIMP IRREDUCIBLE) 1 $X)) MAXIMA> (to-maxima)
Returning to Maxima
(%o2) true
(%i3) result;
(%o3) x (x + 1)
[System variable]
values
Initial value: []
values is a list of all bound user variables (not Maxima options or switches). The list comprises symbols bound by :, or::.
If the value of a variable is removed with the commands kill,remove, orremvalue the variable is deleted fromvalues.
Seefunctions for a list of user defined functions.
Examples:
First, valuesshows the symbols a, b, and c, but not d, it is not bound to a value, and not the user function f. The values are removed from the variables. values is the empty list.
(%i1) [a:99, b:: a-90, c:a-b, d, f(x):=x^2];
2 (%o1) [99, 9, 90, d, f(x) := x ] (%i2) values;
(%o2) [a, b, c]
(%i3) [kill(a), remove(b,value), remvalue(c)];
(%o3) [done, done, [c]]
(%i4) values;
(%o4) []
4.3 Functions and Variables for Display
[Option variable]
%edispflag
Default value: false
When%edispflagistrue, Maxima displays%eto a negative exponent as a quotient.
For example,%e^-x is displayed as1/%e^x. See also exptdispflag.
Example:
(%i1) %e^-10;
- 10
(%o1) %e
(%i2) %edispflag:true$
(%i3) %e^-10;
1
(%o3) ----
10
%e
[Option variable]
absboxchar
Default value: !
absboxchar is the character used to draw absolute value signs around expressions which are more than one line tall.
Example:
(%i1) abs((x^3+1));
! 3 !
(%o1) !x + 1!
[Function]
declare_index_properties (a, [p_1, p_2, p_3, ...])
[Function]
declare_index_properties ([a, b, c, ...], [p_1, p_2, p_3, ...])
[Symbol]
postsubscript
[Symbol]
postsuperscript
[Symbol]
presuperscript
[Symbol]
presubscript
Declares the properties of indices applied to the symbol a or each of the of symbols a, b,c, .... If multiple symbols are given, the whole list of properties applies to each symbol.
Given a symbol with indices, a[i_1,i_2,i_3, ...], thek-th propertyp k applies to thek-th indexi k. There may be any number of index properties, in any order.
Each property p k must one of these four recognized properties: postsubscript, postsuperscript, presuperscript, or presubscript, to denote indices which are displayed, respectively, to the right and below, to the right and above, to the left and above, or to the left and below.
Index properties apply only to the 2-dimensional display of indexed variables (i.e., when display2d is true) and TeX output via tex. Otherwise, index properties are ignored. Index properties do not change the input of indexed variables, do not change the algebraic properties of indexed variables, and do not change the 1-dimensional display of indexed variables.
declare_index_properties quotes (does not evaluate) its arguments.
remove_index_propertiesremoves index properties. killalso removes index prop- erties (and all other properties).
get_index_propertiesretrieves index properties.
Examples:
Given a symbol with indices, a[i_1,i_2,i_3, ...], thek-th propertyp k applies to thek-th indexi k. There may be any number of index properties, in any order.
(%i1) declare_index_properties (A, [presubscript, postsubscript]);
(%o1) done
(%i2) declare_index_properties (B, [postsuperscript, postsuperscript, presuperscript]);
(%o2) done
(%i3) declare_index_properties (C, [postsuperscript, presubscript, presubscript, presuperscript]);
(%o3) done
(%i4) A[w, x];
(%o4) A
w x (%i5) B[w, x, y];
y w, x
(%o5) B
(%i6) C[w, x, y, z];
z w
(%o6) C
x, y
Index properties apply only to the 2-dimensional display of indexed variables and TeX output. Otherwise, index properties are ignored.
(%i1) declare_index_properties (A, [presubscript, postsubscript]);
(%o1) done
(%i2) A[w, x];
(%o2) A
w x (%i3) tex (A[w, x]);
$${}_{w}A_{x}$$
(%o3) false
(%i4) display2d: false $ (%i5) A[w, x];
(%o5) A[w,x]
(%i6) display2d: true $ (%i7) grind (A[w, x]);
A[w,x]$
(%o7) done
(%i8) stringdisp: true $ (%i9) string (A[w, x]);
(%o9) "A[w,x]"
[Function]
get_index_properties (a)
Returns the properties for aestablished by declare_index_properties.
See also remove_index_properties.
[Function]
remove_index_properties (a, b, c, ...)
Removes the properties established by declare_index_properties. All index prop- erties are removed from each symbol a,b,c, ....
remove_index_propertiesquotes (does not evaluate) its arguments.
[Symbol property]
display_index_separator
When a symbol A has index display properties declared via declare_index_
properties, the value of the property display_index_separator is the string or other expression which is displayed between indices.
The value of display_index_separator is assigned by put(A,S, display_index_
separator), where S is a string or other expression. The assigned value is retrieved by get(A, display_index_separator).
The display index separator S can be a string, including an empty string, or false, indicating the default separator, or any expression. If not a string and notfalse, the property value is coerced to a string viastring.
If no display index separator is assigned, the default separator is used. The default separator is a comma. There is no way to change the default separator.
Each symbol has its own value of display_index_separator.
See also put,get, anddeclare_index_properties.
Examples:
When a symbol A has index display properties, the value of the property display_
index_separatoris the string or other expression which is displayed between indices.
The value is assigned by put(A,S, display_index_separator),
(%i1) declare_index_properties (A, [postsuperscript, postsuperscript, presubscript, presubscript]);
(%o1) done
(%i2) put (A, ";", display_index_separator);
(%o2) ;
(%i3) A[w, x, y, z];
w;x
(%o3) A
y;z
The assigned value is retrieved byget(A, display_index_separator).
(%i1) declare_index_properties (A, [postsuperscript, postsuperscript, presubscript, presubscript]);
(%o1) done
(%i2) put (A, ";", display_index_separator);
(%o2) ;
(%i3) get (A, display_index_separator);
(%o3) ;
The display index separator S can be a string, including an empty string, or false, indicating the default separator, or any expression.
(%i1) declare_index_properties (A, [postsuperscript, postsuperscript, presubscript, presubscript]);
(%o1) done
(%i2) A[w, x, y, z];
w, x
(%o2) A
y, z
(%i3) put (A, "-", display_index_separator);
(%o3) -
(%i4) A[w, x, y, z];
w-x
(%o4) A
y-z
(%i5) put (A, " ", display_index_separator);
(%o5)
